Learning Objectives: Define and calculate default correlation for credit portfolios. Identify drawbacks in using the correlation-based credit portfolio framework. Assess the impact of correlation on a credit portfolio and its Credit VaR. Describe the use of a single-factor model to measure portfolio credit risk, including the impact of correlation.
Questions:
24.11.1: An investment firm has exposure to two credits. The first credit, rated BBB, has a default probability of 0.003 over the time horizon t, while the second credit, rated CCC, has a default probability of 0.005 over a comparable horizon. The combined default probability for both credits over the time horizon t is 0.0002. Calculate the default correlation for this portfolio.
a. 0.04796
b. 0.00262
c. 0.00338
d. 0.04796
24.11.2: Imagine a bank that has a diversified portfolio of corporate bonds. They use historical default correlation data among different sectors to assess the overall risk of their portfolio. Which of the following BEST illustrates the drawback of using the correlation-based credit portfolio framework?
a. The bank experiences a significant loss due to a sudden default in one of its bond holdings, despite having low default correlation with the rest of the portfolio.
b. The bank's portfolio performs exceptionally well during a period of economic downturn, contradicting the correlation-based risk assessment.
c. Despite having high default correlation among certain sectors, the bank's portfolio experiences minimal losses during a financial crisis.
d. The bank reallocates its investments based solely on historical default correlation data, leading to increased exposure to individual asset risks.
24.11.3: In the portfolio, there are 50 credits with a combined value of $50,000,000. This indicates that each credit holds a face value of $1,000,000 in the absence of default. The default correlation is 0 and = 0.015, and the number of defaults is binomially distributed with parameters n = 50 and = 0.015. The 95th percentile corresponds to 7 defaults. Find the credit Value at Risk (VaR) of this distribution.
a. $6,000,000
b. $750,000
c. $4,500,000
d. $5,250,000
Answers here:
Questions:
24.11.1: An investment firm has exposure to two credits. The first credit, rated BBB, has a default probability of 0.003 over the time horizon t, while the second credit, rated CCC, has a default probability of 0.005 over a comparable horizon. The combined default probability for both credits over the time horizon t is 0.0002. Calculate the default correlation for this portfolio.
a. 0.04796
b. 0.00262
c. 0.00338
d. 0.04796
24.11.2: Imagine a bank that has a diversified portfolio of corporate bonds. They use historical default correlation data among different sectors to assess the overall risk of their portfolio. Which of the following BEST illustrates the drawback of using the correlation-based credit portfolio framework?
a. The bank experiences a significant loss due to a sudden default in one of its bond holdings, despite having low default correlation with the rest of the portfolio.
b. The bank's portfolio performs exceptionally well during a period of economic downturn, contradicting the correlation-based risk assessment.
c. Despite having high default correlation among certain sectors, the bank's portfolio experiences minimal losses during a financial crisis.
d. The bank reallocates its investments based solely on historical default correlation data, leading to increased exposure to individual asset risks.
24.11.3: In the portfolio, there are 50 credits with a combined value of $50,000,000. This indicates that each credit holds a face value of $1,000,000 in the absence of default. The default correlation is 0 and = 0.015, and the number of defaults is binomially distributed with parameters n = 50 and = 0.015. The 95th percentile corresponds to 7 defaults. Find the credit Value at Risk (VaR) of this distribution.
a. $6,000,000
b. $750,000
c. $4,500,000
d. $5,250,000
Answers here:
